Geodesic
A General Linear Theory of Elastic Plates and its Variational Validation
Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 2, pp. 321-341.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We provide a variational justification for shearable-plate models that generalize the classic Reissner-Mindlin model. Firstly, we give an argument leading to choose a fairly general linearly elastic monoclinic material response. Secondly, we prove that, for materials in such constitutive class, the variational limit of certain suitably scaled 3D energies is a functional whose minimum over a maximal subspace of admissible functions coincides with the minimum of the generalized Reissner-Mindlin functional. 
@article{BUMI_2009_9_2_2_a1,
     author = {Percivale, Danilo and Podio-Guidugli, Paolo},
     title = {A {General} {Linear} {Theory} of {Elastic} {Plates} and its {Variational} {Validation}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {321--341},
     publisher = {mathdoc},
     volume = {Ser. 9, 2},
     number = {2},
     year = {2009},
     zbl = {1170.74030},
     mrnumber = {2537273},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_2_a1/}
}
TY  - JOUR
AU  - Percivale, Danilo
AU  - Podio-Guidugli, Paolo
TI  - A General Linear Theory of Elastic Plates and its Variational Validation
JO  - Bollettino della Unione matematica italiana
PY  - 2009
SP  - 321
EP  - 341
VL  - 2
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_2_a1/
LA  - en
ID  - BUMI_2009_9_2_2_a1
ER  - 
%0 Journal Article
%A Percivale, Danilo
%A Podio-Guidugli, Paolo
%T A General Linear Theory of Elastic Plates and its Variational Validation
%J Bollettino della Unione matematica italiana
%D 2009
%P 321-341
%V 2
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_2_a1/
%G en
%F BUMI_2009_9_2_2_a1
Percivale, Danilo; Podio-Guidugli, Paolo. A General Linear Theory of Elastic Plates and its Variational Validation. Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 2, pp. 321-341. http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_2_a1/

[1] A. Braides, $\Gamma$-convergence for beginners. Oxford University Press, 2002. | DOI | MR

[2] G. Dal Maso, An Introduction to $\Gamma$-convergence. Birkhäuser, 1993. | DOI | MR

[3] M. E. Gurtin, The Linear Theory of Elasticity. In Handbuch der Physik VIa/2, C. Truesdell Ed., Springer 1972.

[4] G. Lancioni - P. Podio-Guidugli, Dynamics of incoherent elastic slabs. Fortcoming (2008).

[5] M. Lembo - P. Podio-Guidugli, How to use reactive stresses to improve plate-theory approximations of the stress field in a linearly elastic plate-like body. Int. J. Sol. & Struct. 44 (5) (2007), 1337-1369. | DOI | MR | Zbl

[6] B. Miara - P. Podio-Guidugli, Une approche formelle unifiée des théories de plaques et poutres linéairement élastiques. C.R. Acad. Sci. Paris, Ser. I, 343, (2006), 675-678. | DOI | MR | Zbl

[7] B. Miara - P. Podio-Guidugli, Deduction by scaling: a unified approach to classic plate and rod theories. Asympt. Anal., 51 (2) (2007), 113-131. | MR | Zbl

[8] R. Paroni - P. Podio-Guidugli - G. Tomassetti, The Reissner-Mindlin plate theory via $\Gamma$-convergence. C.R. Acad. Sci. Paris, Ser. I, 343 (2006), 437-440. | DOI | MR | Zbl

[9] R. Paroni - P. Podio-Guidugli - G. Tomassetti, A justification of the Reissner-Mindlin plate theory through variational convergence. Anal. 5 (2) (2007), 165-182. | DOI | MR | Zbl

[10] P. Podio-Guidugli, An exact derivation of the thin plate equation. J. Elasticity, 22 (1989), 121-133. | DOI | MR | Zbl

[11] P. Podio-Guidugli, Some recent results on Saint-Venant Problem. Pp. 35-45 of Atti dei Convegni Lincei N. 140, Giornata Lincea su "Il Problema di de Saint-Venant: Aspetti Teorici e Applicativi" (Roma, 6 March 1997). | MR